{"paper":{"title":"Weak saturation numbers of large complete bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ilya Vorobyev, Maksim Zhukovskii, Margarita Akhmejanova","submitted_at":"2025-08-26T21:09:45Z","abstract_excerpt":"An $n$-vertex graph $G$ is weakly $F$-saturated if $G$ contains no copy of $F$ and there exists an ordering of all edges in $E(K_n) \\setminus E(G)$ such that, when added one at a time, each edge creates a new copy of $F$. The minimum size of a weakly $F$-saturated graph $G$ is called the weak saturation number $\\mathrm{wsat}(n, F)$. We obtain exact values and new bounds for $\\mathrm{wsat}(n, K_{s,t})$ in the previously unaddressed range $s+t < n < 3t-3$, where $3\\leq s\\leq t$. To prove lower bounds, we introduce a new method that takes into account connectivity properties of subgraphs of a com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.19435","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.19435/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}